过双曲线x2a2-y2b2=1（a＞0，b＞0）的左焦点F1作x轴的垂线交双曲线_爱下问搜题

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问题填空题

过双曲线

x2

a2

-

y2

b2

=1（a＞0，b＞0）的左焦点F₁作x轴的垂线交双曲线于点P，F₂为右焦点，若∠F₁PF₂=45°，则双曲线的离心率为 ______．

答案

由题设知|PF1|=

b2

a

，

∵∠F₁PF₂=45°，

∴|PF₁|=|F₁F₂|，

∴

b2

a

=2c，

∴c²-a²=2ac，

∴e²-2e-1=0，

∴e=

2

+1或e=-

2

+1（舍0．

故答案为：

2

+1．

阅读理解

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填空题

一台电烤箱额定功率为1.5kW．它正常工作0.5h消耗电能______度．